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Math Help - prime numbers

  1. #1
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    prime numbers

    Hi

    Something i've noticed about prime numbers. If you multiply consecutive prime numbers i.e. 2x3x5=30
    and then add the other consecutive primes you get a prime or a prime x prime.

    30+7= 37
    30+11=41
    30+13=43
    30+17=47
    30+19= 49 (7x7)


    Phil
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: prime numbers

    17*19 + 23 + 29 = 375 which is 5*5*5*3
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  3. #3
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    Re: prime numbers

    I used python to test this out and it quickly became unwieldy, although I managed to get some results.

    Multiplying consecutive primes starting from 2 and adding the last consecutive prime.
    Code:
    6 + 5 = 11     is prime
    30 + 7 = 37     is prime
    210 + 11 = 221     13 * 17
    2310 + 13 = 2323     23 * 101
    30030 + 17 = 30047     is prime
    510510 + 19 = 510529     is prime
    9699690 + 23 = 9699713     is prime
    223092870 + 29 = 223092899     127 * 1231 * 1427    False
    6469693230 + 31 = 6469693261     107 * 787 * 76829    False
    Multiplying consecutive primes and then adding any greater prime.
    Code:
    2x3 = 6
        6 + 5 = 11  ->  is prime
        6 + 7 = 13  ->  is prime
        6 + 11 = 17  ->  is prime
        6 + 13 = 19  ->  is prime
        6 + 17 = 23  ->  is prime
    
    
    2x3x5 = 30
        30 + 7 = 37  ->  is prime
        30 + 11 = 41  ->  is prime
        30 + 13 = 43  ->  is prime
        30 + 17 = 47  ->  is prime
        30 + 19 = 49  ->  7 * 7
    
    
    2x3x5x7 = 210
        210 + 11 = 221  ->  13 * 17
        210 + 13 = 223  ->  is prime
        210 + 17 = 227  ->  is prime
        210 + 19 = 229  ->  is prime
        210 + 23 = 233  ->  is prime
    
    
    2x3x5x7x11 = 2310
        2310 + 13 = 2323  ->  23 * 101
        2310 + 17 = 2327  ->  13 * 179
        2310 + 19 = 2329  ->  17 * 137
        2310 + 23 = 2333  ->  is prime
        2310 + 29 = 2339  ->  is prime
    
    
    2x3x5x7x11x13 = 30030
        30030 + 17 = 30047  ->  is prime
        30030 + 19 = 30049  ->  151 * 199
        30030 + 23 = 30053  ->  41 * 733
        30030 + 29 = 30059  ->  is prime
        30030 + 31 = 30061  ->  23 * 1307
    
    
    2x3x5x7x11x13x17 = 510510
        510510 + 19 = 510529  ->  is prime
        510510 + 23 = 510533  ->  83 * 6151
        510510 + 29 = 510539  ->  31 * 43 * 383    False
        510510 + 31 = 510541  ->  307 * 1663
        510510 + 37 = 510547  ->  139 * 3673
    
    
    2x3x5x7x11x13x17x19 = 9699690
        9699690 + 23 = 9699713  ->  is prime
        9699690 + 29 = 9699719  ->  47 * 47 * 4391    False
        9699690 + 31 = 9699721  ->  23 * 421727
        9699690 + 37 = 9699727  ->  is prime
        9699690 + 41 = 9699731  ->  is prime
    
    
    2x3x5x7x11x13x17x19x23 = 223092870
        223092870 + 29 = 223092899  ->  127 * 1231 * 1427    False
        223092870 + 31 = 223092901  ->  43 * 5188207
        223092870 + 37 = 223092907  ->  is prime
        223092870 + 41 = 223092911  ->  29 * 29 * 265271    False
        223092870 + 43 = 223092913  ->  6971 * 32003
    I thought I might as well post it.

    Could only find 6 occurrences where this was False. This is a small sample, but I think you were on to something, at least for a quick way of finding a number which is likely prime or semi-prime.
    Last edited by russ123; November 19th 2012 at 10:47 AM.
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